Development and application of the Kalman filter ... - IRTG Heidelberg

Development and application
of the Kalman filter method
in the CBM and ALICE experiments
Sergey Gorbunov
GSI / KIP
Heidelberg
October 19, 2007

Outline
• Fit problem in event reconstruction in HEP
• The Kalman Filter method
• Kalman Filter for on-line event reconstruction in CBM
• KF track fit in CBM
• CA+KF tracker in CBM
• Fast SIMDized Kalman Filter
• Kalman Filter for on-line event reconstruction in ALICE HLT
• CA tracker for ALICE HLT
• KF fit with 3D track model
• Reconstruction of vertices and decayed particles
• Summary
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 2/15

Fit problem in event reconstruction
• Track finding
• Track fitting
• Track merging
• Reconstruction of vertices
and decayed particles
D 0 K -
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 3/15
ππ ++

The Kalman filter method
r 0
initial
track
m 1
σ 1
σ m1
r 1
m 2
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 4/15
r 2
m 3
r 3
fitted track
The Kalman filter is the most used method for the fit problem.
The method is well known in HEP, but in modern experiments
the large amount of data and specific problems require development of new
Kalman filter-based algorithms as well as investigations of the basic method.

KF fit in the CBM experiment
The full set of fitting utilities
has been developed
Tracking in STS
Tracking in muon chambers
Tracking in TRD
Track-ring match in RICH
Hit gathering (MVD)
Global tracking
Reconstruction of vertices
and decayed particles
Smoother utility
CBM reconstruction challenge
~ 1000 charged particles/collision
85% fake hits
non-homogeneous magnetic field
10 7 Au+Au collisions/sec
no simple trigger
CbmKF is the default fitting package in CBM
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 5/15

CA+KF tracker for CBM
CA w/o KF CA with KF
Efficiency, %
95.29
90.52
76.05
0.00
2.18
Track category
Reference set
All set
Extra set
Clone
Ghost
Efficiency, %
99.45
96.98
89.46
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 6/15
0.01
0.61

Speed up of the Kalman filter
Problem: Pixel geometry (1 sec ) => double-sided strips (3 min)
Reco time = N combinations*fit time => speed up of KF fit utilities needed
Stage
0
1
2
3
4
5
6
Initial scalar version
Approximation of the magnetic field
Optimization of the algorithm
SIMDization
Porting to SPE
Parallelization on 16 SPE’s
Final SIMDized version on Cell
FPGA
Description
Time/track
12 ms
240 µs
7.2 µs
1.6 µs
1.1 µs
0.1 µs
0.1 µs
? ns
Speedup
120000
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 7/15
-
50
35
4.5
1.5
10
?
Dual Cell Blade
at the IBM Laboratory,
Böblingen, Germany
Future,
but realistic

KF fit on different architectures
Fit of a single track:
lxg1411
eh102
blade11bc4
S.Gorbunov, U.Kebschull, I.Kisel, V.Lindenstruth, W.F.J.Müller, Fast SIMDized Kalman filter based track fit, acc. by CPC
Fit of thousands of tracks:
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 8/15

Speed up of CA+KF tracker
1000 times
faster
Central events Minimum bias events
Efficiency, %
97.04
93.26
79.95
1.15
2.28
523
78 ms
All set
Clone
Ghost
Track category
Reference set (>1 GeV/c)
Extra set (

CA+KF tracker for ALICE HLT
All Set
(Hits >10, P > .05)
Eff Clone
97.4
14.2
Reference Set
(All Set + P>1.)
Eff Clone
99.5
0.00
Extra Set
(All Set + P

CA+KF algorithm (sector view)
step 0: Clusters
YX view
ZX view
step 1: Cells
YX view
step 2: Neighbors step 3: Tracks ( KF )
• No vertex constraint => physics, cosmics, beam gas, laser tracks…
• Simple code, small memory => Cell, GPU,…
• 3D track model r [8] = ( x, y, z, p x , p y , p z , q/P )
ZX view
ZX view
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 11/15

Reconstruction of vertices and decayed particles
D 0
K -
ππ ++
KFParticle: particle parameters
r [8] = ( x y z, p x p y p z , E, S(=L/p) )
with full covariance matrix C [ 8×8 ]
• Physical track model for mother [D 0 ] and daughters [ππ ++ , K - ]
• State vector contains all the particle parameters
both at decay and production vertices
• Algorithm is suitable for vertex fit ( including primary vertex fit )
• User friendly interface: class CbmKFParticle / AliKFParticle ;
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 12/15

CbmKFParticle performance for D 0 fit in CBM
D 0
10 6 events
Accuracy
Pull
Production Vertex [µm]
x
0.81
1.14
y
0.73
1.10
z
5.50
1.11
x
2.64
1.13
K -
ππ ++
Decay Vertex [µm]
y
2.64
1.13
• Fixed target geometry
• Non-uniform magnetic field
• ~500 primary tracks
63.88
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 13/15
z
1.10
P [%]
0.79
1.20
Physical Parameters
M [MeV/c]
11.34
1.19
L [µm]
64.10
1.11
cT [µm]
9.81
1.11

AliKFParticle performance for D 0 fit in ALICE
10 6 events
Accuracy
Pull
x
61.89 49.07
0.96 0.95
D 0
Production Vertex [µm]
y
60.95 48.79
0.98 0.95
z
87.52 67.42
1.01 0.98
x
100.6 75.41
0.97 0.92
Decay Vertex [µm]
y
K -
75.03 97.4
0.97 0.92
116.1 88.6
• Collider geometry
• Uniform magnetic field
• ~5 primary tracks
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 14/15
ππ ++
z
1.00 0.97
V 0 fit time: 50 µs => HLT
P [%]
0.78 0.75
0.94 0.92
Physical Parameters
M [MeV/c]
10.4 9.9
0.95 0.94
CbmKFParticle = AliKFParticle => same code!
L [µm]
187.3 165.5
0.98 0.93
cT [µm]
115.3 100.4
0.98 0.93

Summary
• Developed and implemented:
The Kalman filter utilities for CBM reconstruction [ σP = 1.2% ]
Fast SIMDized Kalman filter for CBM on-line reconstruction [ 1.6 µs / 0.1 µs ]
CA+KF tracker for CBM [ Eff = 97%, 78 ms / 5 ms ]
CA+KF tracker for ALICE HLT [ Eff = 99%, 100 ms ]
Reconstruction of decayed particles for CBM and ALICE [σcT= 9.8 µm/100 µm, 50 µs]
• Related publications :
• S.Gorbunov, I.Kisel, Analytic formula for track extrapolation in non-homogeneous magnetic field, NIM A 559, (2006)
• S.Gorbunov, U.Kebschull, I.Kisel, V.Lindenstruth, W.F.J.Müller, Fast SIMDized Kalman filter based track fit, CPC, (2007)
• S.Gorbunov, I.Kisel, Primary vertex fit based on the Kalman filter, CBM-SOFT-note-2006-001, (2006)
• S.Gorbunov, I.Kisel, Secondary vertex fit based on the Kalman filter, CBM-SOFT-note-2006-002, (2006)
• S.Gorbunov, I.Kisel, Reconstruction of decayed particles based on the Kalman filter, CBM-SOFT-note-2007-003, (2007)
• S.Gorbunov, I.Kisel, I.Vassiliev, Analysis of D0 detection in Au+Au collisions at 25 AGeV, CBM-PHYS-note-2005-001, (2005)
• S.Gorbunov, I.Kisel, Elastic net for stand-alone RICH ring finding, NIM A 559, (2006)
• Future plans (ALICE HLT):
Track fit investigation
Speed up and SIMDization
Run the reconstruction core on the Cell processor and GPU
Test on heavy ion events
Heidelberg, 19.10.2007 Sergey Gorbunov, GSI/KIP 15/15